If you've split your labelled data into folders then you can scan through several thumbnails at once to catch any misclassified pictures.
Rinse and repeat until the model is good enough.
This might be the most practical way to approach this, but it's not really a fundamental improvement since you still need to consider every image (also the correctly labeled ones).
Not necessarily. The classifier will not only tell you whether it sees a rat, but also its confidence. So you can manually classify just the low confidence images, retrain, and repeat until there's none left or you're happy with its detection rate.
And what if he gets a new cat, or his cat switches to a different kind of prey?
From the outside, it might seem as if he is enslaved by his pet.
I don't see the issue, this is the explicit contract of having a cat for a pet.
I think many first-time cat slaves would disagree